Preheat the oven to 350F.,Bring a large saucepan of water to a boil; add salt.,Add the pasta, and cook until al dente, 8 to 10 minutes.,Drain, transfer to a medium bowl, and toss with 1 tablespoon butter.,Cover, and keep warm while proceeding.,Spread the walnuts on a baking sheet, place in the oven, and toast until fragrant, about 10 minutes.,When cool enough to handle, chop coarsely; set aside.,Place 1/2 cup butter in a small saucepan over medium-high heat.,______,Strain, discarding the solids, into a glass measuring cup or a small bowl, and set aside.,Heat the remaining 2 tablespoons butter in a large skillet over medium heat.,Add the onion and garlic, and cook until they start to soften, about 2 minutes.,Add the sprout leaves, sprinkle with salt, pepper, and herbs, and continue cooking until the leaves are bright green and tender and the onions are translucent, 3 to 5 minutes.,Add the pasta to the skillet, and drizzle with the brown butter.,Toss to combine, and cook until warmed through, seasoning with salt and pepper if needed.,Transfer to a serving dish, and garnish with walnuts and Parmesan cheese.,Serve immediately.